In the prior art it is known to honor priority request signals from a plurality of requestors on a pre-emptive basis. In this pre-emptive selection method, the R requestors R-1 through 0 are assigned priority in a numerically descending ordered manner in which priority selection is from the highest ordered priority requestor R-1 through to the lowest ordered priority requestor 0 last. One example of a pre-emptive selection priority system is that of the Henzel, et al, Pat. No. 3,832,692. In such a system the lower ordered requestors may wait an inordinate period of time for their priority request signals to be honored. The present invention is directed toward a novel priority system in which the last-honored higher-ordered requestor may be rotated in priority with another lower-ordered requestor such that the lower-ordered requestor may be given temporary priority over the last-honored higher-ordered requestor.